13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- The monochromatic X-ray beam at the photon energy of 17.99keV was used and collimated to the spot size of 0.5× 0.5mm2. The beam was incident at the sample perpendicular to its loading direction. Two separate WAXS and SAXS detectors were alternately setup to collect the patterns at consecutive loading increments downstream of the beam. WAXS patterns were recorded using a Photonic Science Image Star 9000 detector (Photonic Science Ltd., UK) with a sample-to-camera distance of 128.72mm. Further downstream, a Pilatus 300K detector (Dectris, Baden, Switzerland) was positioned at a distance of 4358.47mm to collect SAXS patterns. In order to record both WAXS and SAXS patterns at each scanning location, the WAXS detector was translated laterally to expose the SAXS detector after each WAXS exposure. A lightly compacted disk of standard silicon powder and a dry chicken collagen sample inserted close to the sample position were used as calibration standards, and to determine the sample-to-detector distance to good precision. 2.3. Scattering data analysis 2.3.1. WAXS data analysis WAXS data can be interpreted in terms of the shift of the diffraction peak obtained from a cluster of HAp crystals, so that the average micro-strain (lattice strain) in the crystals can be deduced [8,9]. The typical WAXS pattern of HAp is shown in Fig. 2 (only the (002) peak is selected for interpretation). The apparent elastic lattice strain of the HAp phase was computed by observing the changes in the interplanar spacing between the lattice planes [21]: 0 002 002 0 002 d d d ε − = (1) where 002 d is the deformed d-spacing and 0 002 d is the reference strain-free value. In detail, 2D diffraction images were firstly pre-processed using Fit2D [22]. The (002) peak of interest from each pattern was “caked” (i.e. binned in the radial-azimuthal coordinates) within a range of 20o in the loading direction (Fig. 2a). Subsequently the 1D radial plot of intensity within each sector was fitted with Gaussian to obtain the peak centre position. As the load increase, the peak centre position shift with respect to the strain-free reference point allowed the calculation of HAp elastic lattice strain. In addition, the structural orientation angle was determined from the strain-free sample by azimuthal-radial “caking” of the (002) peak over the entire range of 360o, and fitting the azimuthal centre position of the pronounced peaks [23]. 2.3.2. SAXS data analysis For SAXS data analysis, the pattern from the strain-free sample was taken as reference. Due to the dense distribution of crystals in enamel, the electron density changes that occur in the gaps between crystalline particles gives rise to the scattering signal [24]. It is also understood that the orientation of the gaps between rods roughly coincides with the orientation of the crystals within the rod [19]. Thus, the information from gap scattering can be used to deduce the orientation and degree of alignment (percentage of aligned particles) of HAp crystals. To quantify it, the 2D SAXS patterns were processed by integrating over the entire relevant range of scattering vector q, resulting in a function ( ) I ϕ of the azimuthal angle ϕ [25,26]. The predominant orientation 0ϕ of the mineral crystals is determined by the position of the two peaks in the plot of ( ) I ϕ. Further, the degree of alignment ρcan be calculated by the ratio of the two areas under the curve of ( ) I ϕ:
RkJQdWJsaXNoZXIy MjM0NDE=